2003 AACTM Lewis-Parker Lecturer
Prof. Olav Kallenberg
Auburn University
Lewis-Parker Lecture
Title: The Basic Symmetries of Probability Theory
Abstract: We consider random sequences or processes whose
distributions are
invariant under certain groups (or semigroups) of transformations. Three
such symmetries---invariance under contractions, permutations, and
rotations---turn out to be especially fundamental, and their study leads
to a rich theory that relates to practically every other branch of modern
probability theory.
It is impossible in a short talk to do justice to such a vast area of
research. (The speaker is currently writing a monograph on the theory that
will easily run to some 500 pages.) Our present aim is only to discuss, in
broad and elementary terms, some basic connections between the various
symmetries, some relations to classical analysis, and some surprising
applications to gambling and sampling. We hope to conclude with a brief
sketch of the more advanced multivariate theory.
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Ph.D. from Chalmers University, Gothenburg, Sweden, 1972
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After various teaching and research positions at Swedish universities,
came to the US in 1985 and to Auburn in 1986 as a Professor of Mathematics
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In 1977 became the second recipient ever of the prestigious Rollo Davidson
Prize from Cambridge University
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Editor-in-Chief of Probability Theory and Related Fields 1991-94. Had then
been a member of the editorial board since 1976
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Plenary speaker at the 2nd World Congress of the Bernoulli Society of
Mathematical Statistics and Probability, 1990
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One-hour lecturer of the AMS, 1993
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Elected Fellow of the Institute of Mathematical Statistics
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Has published about 70 research papers and two books:
"Random Measures", 4th edition, Akademie-Verlag & Academic Press 1986
"Foundation of Modern Probability", 2nd edition, Springer-Verlag 2002
(The latter book has also appeared in a reprint edition, Beijing 2001, and
in a study edition, Hong Kong 2003.)
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Family: Wife Jinsoo and four children, ages 7-18.
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Special interests: Classical music, cultural history, downhill skiing